"""
Gradient Descent Optimizers
==========================

This module implements various gradient descent optimization algorithms
with proper mathematical formulations and PyTorch compatibility.

Algorithms implemented:
- SGD (Stochastic Gradient Descent)
- Adam (Adaptive Moment Estimation)
- AdamW (Adam with Decoupled Weight Decay)

All optimizers follow the mathematical principles and include proper
momentum, learning rate scheduling, and weight decay handling.
"""

import math
import logging
from abc import ABC, abstractmethod
from typing import Dict, List, Tuple, Any
import torch

logger = logging.getLogger(__name__)


class Optimizer(ABC):
    """Abstract base class for all optimizers"""
    
    def __init__(self, params: List[torch.Tensor], lr: float = 1e-3, **kwargs):
        self.params = params
        self.lr = lr
        self.step_count = 0
        self.state = {}
        
    @abstractmethod
    def step(self, closure=None):
        """Perform a single optimization step"""
        pass
        
    def zero_grad(self):
        """Zero the gradients of all parameters"""
        for param in self.params:
            if param.grad is not None:
                param.grad.zero_()
                
    def state_dict(self):
        """Return the state of the optimizer"""
        return {
            'state': self.state,
            'param_groups': [{'params': self.params, 'lr': self.lr}],
            'step_count': self.step_count
        }
        
    def load_state_dict(self, state_dict):
        """Load the state of the optimizer"""
        self.state = state_dict['state']
        self.lr = state_dict['param_groups'][0]['lr']
        self.step_count = state_dict['step_count']


class SGD(Optimizer):
    """
    Stochastic Gradient Descent optimizer
    
    Mathematical formulation:
    θ_{t+1} = θ_t - α * ∇_θ J(θ_t)
    
    With momentum:
    v_{t+1} = μ * v_t + ∇_θ J(θ_t)
    θ_{t+1} = θ_t - α * v_{t+1}
    """
    
    def __init__(self, params: List[torch.Tensor], lr: float = 1e-3, 
                 momentum: float = 0.0, weight_decay: float = 0.0, 
                 dampening: float = 0.0, nesterov: bool = False):
        super().__init__(params, lr)
        self.momentum = momentum
        self.weight_decay = weight_decay
        self.dampening = dampening
        self.nesterov = nesterov
        
        # Initialize momentum buffers
        for param in self.params:
            if momentum > 0:
                self.state[param] = {'momentum_buffer': torch.zeros_like(param)}
                
        logger.info(f"Initialized SGD optimizer: lr={lr}, momentum={momentum}, weight_decay={weight_decay}")
    
    def step(self, closure=None):
        """Perform SGD optimization step"""
        loss = None
        if closure is not None:
            loss = closure()
            
        for param in self.params:
            if param.grad is None:
                continue
                
            grad = param.grad.data
            
            # Apply weight decay
            if self.weight_decay != 0:
                grad = grad.add(param.data, alpha=self.weight_decay)
            
            # Apply momentum
            if self.momentum != 0:
                param_state = self.state[param]
                if 'momentum_buffer' not in param_state:
                    param_state['momentum_buffer'] = torch.zeros_like(param.data)
                
                momentum_buffer = param_state['momentum_buffer']
                momentum_buffer.mul_(self.momentum).add_(grad, alpha=1 - self.dampening)
                
                if self.nesterov:
                    grad = grad.add(momentum_buffer, alpha=self.momentum)
                else:
                    grad = momentum_buffer
            
            # Update parameters
            param.data.add_(grad, alpha=-self.lr)
            
        self.step_count += 1
        return loss


class Adam(Optimizer):
    """
    Adam (Adaptive Moment Estimation) optimizer
    
    Mathematical formulation:
    m_t = β₁ * m_{t-1} + (1 - β₁) * g_t
    v_t = β₂ * v_{t-1} + (1 - β₂) * g_t²
    m̂_t = m_t / (1 - β₁ᵗ)
    v̂_t = v_t / (1 - β₂ᵗ)
    θ_{t+1} = θ_t - α * m̂_t / (√v̂_t + ε)
    """
    
    def __init__(self, params: List[torch.Tensor], lr: float = 1e-3,
                 betas: Tuple[float, float] = (0.9, 0.999), eps: float = 1e-8,
                 weight_decay: float = 0.0, amsgrad: bool = False):
        super().__init__(params, lr)
        self.betas = betas
        self.eps = eps
        self.weight_decay = weight_decay
        self.amsgrad = amsgrad
        
        # Initialize moment estimates
        for param in self.params:
            self.state[param] = {
                'step': 0,
                'exp_avg': torch.zeros_like(param.data),
                'exp_avg_sq': torch.zeros_like(param.data)
            }
            if amsgrad:
                self.state[param]['max_exp_avg_sq'] = torch.zeros_like(param.data)
                
        logger.info(f"Initialized Adam optimizer: lr={lr}, betas={betas}, eps={eps}")
    
    def step(self, closure=None):
        """Perform Adam optimization step"""
        loss = None
        if closure is not None:
            loss = closure()
            
        for param in self.params:
            if param.grad is None:
                continue
                
            grad = param.grad.data
            
            # Apply weight decay
            if self.weight_decay != 0:
                grad = grad.add(param.data, alpha=self.weight_decay)
            
            param_state = self.state[param]
            exp_avg, exp_avg_sq = param_state['exp_avg'], param_state['exp_avg_sq']
            beta1, beta2 = self.betas
            
            param_state['step'] += 1
            bias_correction1 = 1 - beta1 ** param_state['step']
            bias_correction2 = 1 - beta2 ** param_state['step']
            
            # Update biased first moment estimate
            exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
            
            # Update biased second raw moment estimate
            exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
            
            if self.amsgrad:
                # Maintains the maximum of all 2nd moment running avg. of squared gradients
                torch.max(param_state['max_exp_avg_sq'], exp_avg_sq, out=param_state['max_exp_avg_sq'])
                # Use the max. for normalizing running avg. of squared gradients
                denom = (param_state['max_exp_avg_sq'].sqrt() / math.sqrt(bias_correction2)).add_(self.eps)
            else:
                denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(self.eps)
            
            # Update parameters
            step_size = self.lr / bias_correction1
            param.data.addcdiv_(exp_avg, denom, value=-step_size)
            
        self.step_count += 1
        return loss


class AdamW(Optimizer):
    """
    AdamW (Adam with Decoupled Weight Decay) optimizer
    
    Mathematical formulation:
    θ_t = θ_{t-1} - α * (m̂_t / (√v̂_t + ε) + λ * θ_{t-1})
    
    Where weight decay is applied directly to parameters, not gradients.
    """
    
    def __init__(self, params: List[torch.Tensor], lr: float = 1e-3,
                 betas: Tuple[float, float] = (0.9, 0.999), eps: float = 1e-8,
                 weight_decay: float = 0.01, amsgrad: bool = False):
        super().__init__(params, lr)
        self.betas = betas
        self.eps = eps
        self.weight_decay = weight_decay
        self.amsgrad = amsgrad
        
        # Initialize moment estimates
        for param in self.params:
            self.state[param] = {
                'step': 0,
                'exp_avg': torch.zeros_like(param.data),
                'exp_avg_sq': torch.zeros_like(param.data)
            }
            if amsgrad:
                self.state[param]['max_exp_avg_sq'] = torch.zeros_like(param.data)
                
        logger.info(f"Initialized AdamW optimizer: lr={lr}, betas={betas}, weight_decay={weight_decay}")
    
    def step(self, closure=None):
        """Perform AdamW optimization step"""
        loss = None
        if closure is not None:
            loss = closure()
            
        for param in self.params:
            if param.grad is None:
                continue
                
            grad = param.grad.data
            param_state = self.state[param]
            exp_avg, exp_avg_sq = param_state['exp_avg'], param_state['exp_avg_sq']
            beta1, beta2 = self.betas
            
            param_state['step'] += 1
            bias_correction1 = 1 - beta1 ** param_state['step']
            bias_correction2 = 1 - beta2 ** param_state['step']
            
            # Update biased first moment estimate
            exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
            
            # Update biased second raw moment estimate
            exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
            
            if self.amsgrad:
                # Maintains the maximum of all 2nd moment running avg. of squared gradients
                torch.max(param_state['max_exp_avg_sq'], exp_avg_sq, out=param_state['max_exp_avg_sq'])
                # Use the max. for normalizing running avg. of squared gradients
                denom = (param_state['max_exp_avg_sq'].sqrt() / math.sqrt(bias_correction2)).add_(self.eps)
            else:
                denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(self.eps)
            
            # Update parameters with decoupled weight decay
            step_size = self.lr / bias_correction1
            param.data.mul_(1 - self.lr * self.weight_decay)
            param.data.addcdiv_(exp_avg, denom, value=-step_size)
            
        self.step_count += 1
        return loss


class OptimizerFactory:
    """Factory class for creating optimizers"""
    
    @staticmethod
    def create_optimizer(optimizer_type: str, params: List[torch.Tensor], **kwargs) -> Optimizer:
        """Create an optimizer instance"""
        optimizers = {
            'sgd': SGD,
            'adam': Adam,
            'adamw': AdamW
        }
        
        if optimizer_type.lower() not in optimizers:
            raise ValueError(f"Unknown optimizer type: {optimizer_type}")
            
        optimizer_class = optimizers[optimizer_type.lower()]
        return optimizer_class(params, **kwargs)
    
    @staticmethod
    def get_default_config(optimizer_type: str) -> Dict[str, Any]:
        """Get default configuration for optimizer"""
        configs = {
            'sgd': {
                'lr': 1e-3,
                'momentum': 0.9,
                'weight_decay': 1e-4
            },
            'adam': {
                'lr': 1e-3,
                'betas': (0.9, 0.999),
                'eps': 1e-8,
                'weight_decay': 1e-4
            },
            'adamw': {
                'lr': 1e-3,
                'betas': (0.9, 0.999),
                'eps': 1e-8,
                'weight_decay': 0.01
            }
        }
        
        return configs.get(optimizer_type.lower(), {})